"I hear and I forget. I see and I remember. I do and I understand." (Confucius; Chinese thinker and social philosopher)

             This began as a discussion between cousins, to engage their middle school kids during covid (20-21) vacation in guided activities at home. Vidya.T planned the science concepts and I did the math part. We had 5 very enthusiastic children, working hands-on and learning by doing.

This post is my recording of math activities and a rough plan for the same, with models created by the children. The base being another blog which I've recorded previously. (creative360°: 3 Dimension and Spatial Intelligence)

Objective : To use Spatial Reasoning as a tool to encourage mathematical skill development. 

What is Spatial Reasoning?
It is the ability to visualise and understand things in a three dimension.Understanding how different pieces fit together, describing their position and direction, their shapes and sizes, all form part of spatial reasoning.

Workshop 1 (09/01/2021)

Content : Honeycomb, the most intelligent mathematical architecture in nature. Understanding a hexagon, tiling and why honeybees make hexagonal honey combs.

Students will be able to measure and draw a net of Hexagon. The net will be used to form a hexagon, which will be duplicated to form any number of hexagonal honey comb tiles.

Content : Chandraayan 2, understanding the space mission structure and creating 3D models.

Why Chandrayaan 2 -  A milestone in Indian Space Science with fully developed indigenous mission as every design and technology was created by Indian scientists. It was launched on 22 July 2019. Fresh in the memory of children and they coulld easily relate to it.

Workshop 2 (23/01/2021)

Content: Chandrayaan 2, Launcher
Measuring and constructing a Launcher model with cylinders and cones.

Students will be able to draw the net of cylinders (2 different diameters) and cones. They will then attach the same to form a launcher model.

Workshop 3 (06/02/2021)

Content: Chandrayaan 2, Lander
Measuring and constructing a Lander model, understanding Frustum.

Students will be able to draw the net of a Truncated Pyramid/Frustum and create model of 'Vikram Lander'. Well that was like a big step, but hey, they did so well!!!! good job kids....

and more to come.....

Workshop 4 (13/02/2021)

Content: Chandrayaan 2, Lander and Rover
Constructing dome and legs for lander and making rover model.

Students will be finishing the Lander and Rover models by improvising and reusing materials available at home. Get creative guys!!!

Awesome job!!!

Factors and Multiples, LCM & HCF Mind Map

 

Fractions Mindmap

 

Inference and Discovery, the art of understanding.....

 Its Harry Potter time at home and my daughter is parallelly watching the movie and reading the book, literally living that life. Obviously discussions are mostly based on the same.

Suddenly she said, "Ma, death cannot actually be a person. Its a process you see." (Those who are familiar with the 3 deathly hallows story will know that death is personified in this story)

And that is what we call a good Inference!. Inference rules are extremely important in Language Processing, Scientific Discoveries, Artificial Intelligence and many more.

Inferences are based on evidence you can see or collect. - In this case Death is not a person because it has no form, it does not have a life cycle of its own and its a one time event in one's life. img-1                  img-2

In image-1 you see the woolen clothes, cap, scarf, gloves etc and your infer its winter wear.

In image-2 you see umbrella, clouds, boots rainbow and you infer its rainy days.

Making inference to understand concepts, can be a very interesting exercise in the classroom. CHALLENGE THE YOUNG MINDS!!!

Inference | Classroom Strategies | Reading Rockets

inference-science-strategy-guide.pdf (readingrockets.org)

Text Box/Bag Activity -      Math Strategies (weebly.com)

3 Dimension and Spatial Intelligence

Remember the Indian fable “Six Blind men and The Elephant”?. They began to argue and shout about the shape of an elephant. Each one of them insisted that he was right and literally got into a fight. A wise man who was passing by, saw this. What is the problem? he asked. “We cannot agree to what the elephant looks like.” Each one of them told what an elephant looks like according to them. The wise man calmly explained to them. “All of you are right. Elephant is a huge animal. Each one of you touched a different part of the elephant. Elephant has the features each one of you said”.

Though the moral of the story is to highlight the limitations of human perception, it is a beautiful example to define/visualize features of an object.

To get the bigger picture you need to have that leap in perception, to connect the dots, lines and planes….

The everyday world is a 3D (three dimension) space. It has width, depth and height. This is the one we live in, the one we are used to from the day we are born. This is what teaching 3D and 2D is about. “Spatial Awareness”.
In this 3D world you can go forward-backwards, right-left, up-down.
The ability to travel up into space and then dive deep down into the water, differentiated 3D from 2D. 

Progressive approach to teach 3 dimensions to children

https://nzmaths.co.nz/shape-early-learning-progression
Check out the Key Concepts, their importance and Teaching and Learning Points.

Features/Properties of these 3D shapes in Mathematical Vocabulary 

(https://spiritualcollection.files.wordpress.com/ https://www.math-only-math.com/images/)

https://imgv2-1-f.scribdassets.com/img

As children develop their understanding of dimensions this way, they will be able to represent them in different forms. Through drawings, models, words and gestures. (I recollect with great pride the dance on solid shapes we did for our ‘Math Assembly’ in Coimbatore).

Practical applications of 3D - Product design, Remote Surgery, Lay out of Stores, Molecular Science, Photo Realistic Rendering, Movies and many more. 3D modeling is mathematical representation of a object, explaining how the object is put together. It is equal parts of Math, Geometry and Design.

And for those who like a little more… check out this article.https://plus.maths.org/content/mother-all-theories

Maps, Routes and Mathematics

What is a Map? And when did you use a route map lastly? oh, and what does math has to do with maps? Well, lets see.

Long long ago, actually not so long ago, before the google map and GPS we still travelled.👍
We found our way through, in unknown places and yes People discovered places...
The most important tools which we used were The Sun, Moon and the Stars and of course the Cardinal Directions (East, West, North and South). Simple right!.


Focus Points

·       Visualizing objects/space and representing them in a paper

This is a beautiful concept to develop the observational skills among children. I always use the “count and recollect the objects game” for kids. In this game a specific number of things (say 20) are displayed in a room. Kids can observe the object for 10mts and to list them down in a paper, without seeing. Well, one must be conscious about their surrounding right! Now in this concept, you do not just list them down. You draw them out!!! Excellent.

·       Orientation – Relative position of objects in space w.r.t cardinal directions

Age old traditions use nature as relative constant. The Sun, The Moon and Yes “The Pole Star”, which has been the sailors’ compass to reach shores safely (That is opportunity for an interesting narration/story). Where is the north of your classroom and how would you identify that? Once you have done that you can draw the floor map of your classroom, then your school, your community, state, country and what not! But if you do a map without marking your north, what can go wrong?

·       Idea of dimensions (representing big/small objects in picture)

Ok, I got my North right. Its time to put down things in paper. There are different things here. Like the door which is bigger than the window. The benches and chairs and things big and small. How does my eyes perceive them? How can I help other see this in a drawing? Yup get your creative skills do the task. There is no right or wrong, good or bad… just the intention to communicate through picture. Imagine you are helping a new student to navigate your class, now the challenge is you should do this only through drawings.

·       Idea of distance (and scale)

It’s a drawing right, so we put down biiiiiiiiiiiiiiig spaces (I mean length and breadth) in small paper. But be careful with which one should be long/short… have you ever thought, Why are rooms invariably rectangular spaces? (Golden Ratio)


So, Did you discover the “Still Life Artist” in you today?

The key factors to logically approach a destination in the shortest possible time (yup the math of movement) lies in positioning things relatively, with symbols for reference. When kids are taught with these two factors and use natural reference, we are teaching them a survival skill.
Key points to focus
1. Compass rose/Cardinal directions (East, West, North and South)

The figure used to represent the orientation of the cardinal directions, in a map. It can be as simple as just an arrow marking the North, or a elaborate one like this giving all the eight directions. Without a compass rose, your map will not be valid.

2. Symbols (Pictorial representation of Physical Landmarks)

3. Map Key or Legend (helps to understand the map)

(https://clipground.com/images/key-mapping-clipart-3.jpg)

Doing a class activity on map symbols will be fun. Visualisation is a very important skill to understand the language of Nature.


Food for Thought!!!
Indian topography is very ancient. The main sources of ancient Indian geographical works are the Vaidikas, the Ramayana, the Mahabharata, the work of Buddhists, Jains and the Puranas.
The rishis of Rigveda initially formulated the principle of four directions, i.e., Purva (east), Paschima (west), Uttar (north) and Dakshina (south).
By adding Zenith (Meru) and Nadir (Badavanala), it was raised to six. Afterwards eight and ten directions are frequently mentioned in the Puranic literature.

Wondering about Squares and Cubes

G is my friend who comes home, to get help in mathematics. He is extremely passionate and crazy about cricket. He spends close to 5hrs in the ground with his district team. Well, he is in class 8. When we met for the first time, he said he is not able to follow anything in math class, so he usually shuts off. He would be glad if I can help. "My pleasure". I love one-one time specifically for learning. G doesn’t talk much. I must be very sensitive to his very subtle facial expressions to know what he feels. And most of the times he is tired after his cricket practice.


It was a sunny evening and G walked in at 6pm after his field practice. We sat down and after over a cup of fresh mint juice, started with cubes and cube roots (chapter7 NCERT). I was telling him about cubes what they are… And G gave me this very deep thoughtful look!. “why am I learning this?” he slowly asked, Is it really important to know this???????????. I was not sure how answer that question. To me numbers are always exciting, as exciting as playing cricket was for G.

There are just 4 perfect cubes from 1-100. 
1  =1x1x1
8  =2x2x2
27=3x3x3
64=4x4x4

Guess what? cubes were in news recently with a major breakthrough. Diophantus of Alexandria, a 3rd century mathematician had posed the problem of sum of 3 cubes.

x³+y³+z³=k, with k being all the numbers from one to 100.

Looks simple?, well not really. Enjoy reading
This was in 1994
http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math04/matb0100.htm 

Note the "???" for some numbers 

In March 2019 Andrew Booker solved the sum of 3 cubes for 33In September 2019 Professors Andrew Booker and Andrew Sutherland found the solution for 42 by using Charity Engine
https://phys.org/news/2019-09-sum-cubes-solvedusing-real-life.html

Watch them in action!!!
for 42
for 33
for 74